## Taiwanese Journal of Mathematics

### $B$-SEMIPREINVEX FUNCTIONS AND VECTOR OPTIMIZATION PROBLEMS IN BANACH SPACES

#### Abstract

In this paper, we extend the scalar-valued $B$-semipreinvex functions and vector-valued preinvex functions to the cases of vector-valued $B$-semipreinvex functions in Banach spaces. We investigate some properties for the vector-valued $B$-semipreinvex functions and consider a new class of vector-valued nonsmooth programming problems in which functions are locally Lipschitz. In terms of the Ralph vector sub-gradient, we obtain the generalized Kuhn-Tucker type sufficient optimality conditions and saddle point condition. Also, a generalized Mond-Weir type dual is formulated and some duality theorems are established involving locally Lipschitz $B$-semipreinvex functions for the pair of primal and dual programming. The results presented in this paper generalize some main results of Kuang and Batista Dos Santoset, Osuna-Gomez, Rojas-Medar and Rufian-Lizana.

#### Article information

Source
Taiwanese J. Math. Volume 11, Number 3 (2007), 595-609.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404746

Digital Object Identifier
doi:10.11650/twjm/1500404746

Zentralblatt MATH identifier
1194.90113

#### Citation

Chen, Sheng-Lan; Huang, Nan-Jing; Wong, Mu-Ming. $B$-SEMIPREINVEX FUNCTIONS AND VECTOR OPTIMIZATION PROBLEMS IN BANACH SPACES. Taiwanese J. Math. 11 (2007), no. 3, 595--609. doi:10.11650/twjm/1500404746. https://projecteuclid.org/euclid.twjm/1500404746